Summation and multiplication: two distinct operation domains of leaky integrate-and-fire neurons

The spiking frequency of a leaky integrate-and-fire (LIF) neuron can be proportional to the sum or the product of a number n≥2 of input frequencies. In the paper, the parameter domains (discharge time constants and synaptic weights) for these two operation modes are defined theoretically and studied by simulations. Summation is based on the frequency division principle and requires discharge time constant as long as possible. In this mode, the LIF neuron is subject to phase locking effects and is insensitive to the irregularity of the input spike trains. Multiplication is based on coincidence detection and requires shorter time constants. Simulations show that the quality of the mulutiplication function decreases for large irregularities of the input spike trains, that there is an optimum value of the synaptic weights and that there is a consequent input-output frequency level drop. In the brain, the frequency level decrease observed from retina to higher cortical areas might indicate the presence of mult...

[1]  K Fukushima,et al.  Handwritten alphanumeric character recognition by the neocognitron , 1991, IEEE Trans. Neural Networks.

[2]  H. Barlow.  Trigger Features, Adaptation and Economy of Impulses , 1969 .

[3]  Takayuki Ito,et al.  Neocognitron: A neural network model for a mechanism of visual pattern recognition , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  M. Braamhof,et al.  Spatiotemporal correlation in the cerebellum , 1991, IJCNN-91-Seattle International Joint Conference on Neural Networks.

[5]  P. Schwindt,et al.  Factors influencing motoneuron rhythmic firing: results from a voltage-clamp study. , 1982, Journal of neurophysiology.

[6]  M. Ito,et al.  Long-term depression. , 1989, Annual review of neuroscience.

[7]  John H. R. Maunsell,et al.  Visual processing in monkey extrastriate cortex. , 1987, Annual review of neuroscience.

[8]  G. Major,et al.  The modelling of pyramidal neurones in the visual cortex , 1989 .

[9]  Mitsuo Kawato,et al.  Quantitative analysis of electrical properties of dendritic spines , 2004, Biological Cybernetics.

[10]  M. Tsukada,et al.  Stochastic automaton models for the temporal pattern discrimination of nerve impulse sequences , 1976, Biological Cybernetics.

[11]  Matthew A. Wilson,et al.  The simulation of large-scale neural networks , 1989 .

[12]  T. Poggio,et al.  Multiplying with synapses and neurons , 1992 .

[13]  Gen Matsumoto,et al.  Chaos, Phase Locking and Bifurcation in Normal Squid Axons , 1987 .

[14]  W. Levick.  Variation in the response latency of cat retinal ganglion cells. , 1973, Vision research.

[15]  S. Redman.  Quantal analysis of synaptic potentials in neurons of the central nervous system. , 1990, Physiological reviews.

[16]  C. Gross,et al.  Afferent basis of visual response properties in area MT of the macaque. I. Effects of striate cortex removal , 1989, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[17]  A. L. Humphrey,et al.  Spatial and temporal response properties of lagged and nonlagged cells in cat lateral geniculate nucleus. , 1990, Journal of neurophysiology.

[18]  B. Connors,et al.  Intrinsic firing patterns of diverse neocortical neurons , 1990, Trends in Neurosciences.

[19]  Per Bak,et al.  The Devil's Staircase , 1986 .

[20]  Daniel J. Amit,et al.  Attractor neural networks with biological probe records , 1990 .

[21]  E. Vaadia,et al.  Firing patterns of single units in the prefrontal cortex and neural network models , 1990 .

[22]  J. Jack,et al.  The components of synaptic potentials evoked in cat spinal motoneurones by impulses in single group Ia afferents. , 1981, The Journal of physiology.

[23]  M. Soha,et al.  A distributed approach to lan monitoring using intelligent high performance monitors , 1987, IEEE Network.

[24]  H. Wigström,et al.  Shape of frequency-current curves in CAI pyramidal cells in the hippocampus , 1981, Brain Research.

[25]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.